How can I repeat a mesh using multiple empties with unequal distances?
Collection Instances
First put your object(s) into their own collection.
Select all your Empties. Go to the Object Properties, expand the Instancing panel.
Now it is important you keep ALT pressed until the end. This will propagate the modifications to all selected objects.
Click on Collection while still maintaining ALT and choose the collection you want to instance.
If you want &quot;real&quot; meshes afterwards, you can use CTRL + A &gt; Make Instances Real or Object &gt; Apply &gt; Make Instances real.

Troubleshooting :
If you don't see any change after these steps:

Make sure the empties are not in the collection you are trying to instantiate
The Instanced Collection's origin might be different from what you'd expect. You can tweak it by following these steps.
ALT + Click doesn't work because you are emulating a 3 button mouse :

Add a collection instance only for one empty. Select all the other empties too and make sure the instance collection is &quot;active&quot; (yellow outline). Then go to Object &gt; Make Links &gt; Instance Collection or use shortcut CTRL + L.